OrdinalLogisticBiplot (version 0.4)

pordlogist: Ordinal logistic regression with ridge penalization

Description

This function performs a logistic regression between a dependent ordinal variable y and some independent variables x, and solves the separation problem using ridge penalization.

Usage

pordlogist(y, x, penalization = 0.1, tol = 1e-04, maxiter = 200, show = FALSE)

Arguments

y

Dependent variable.

x

A matrix with the independent variables.

penalization

Penalization used to avoid singularities.

tol

Tolerance for the iterations.

maxiter

Maximum number of iterations.

show

Should the iteration history be printed?.

Value

An object of class "pordlogist". This has components:

nobs

Number of observations

J

Maximum value of the dependent variable

nvar

Number of independent variables

fitted.values

Matrix with the fitted probabilities

pred

Predicted values for each item

Covariances

Covariances matrix

clasif

Matrix of classification of the items

PercentClasif

Percent of good classifications

coefficients

Estimated coefficients for the ordinal logistic regression

thresholds

Thresholds of the estimated model

logLik

Logarithm of the likelihood

penalization

Penalization used to avoid singularities

Deviance

Deviance of the model

DevianceNull

Deviance of the null model

Dif

Diference between the two deviances values calculated

df

Degrees of freedom

pval

p-value of the contrast

CoxSnell

Cox-Snell pseudo R squared

Nagelkerke

Nagelkerke pseudo R squared

MacFaden

Nagelkerke pseudo R squared

iter

Number of iterations made

Details

The problem of the existence of the estimators in logistic regression can be seen in Albert (1984); a solution for the binary case, based on the Firth's method, Firth (1993) is proposed by Heinze(2002). All the procedures were initially developed to remove the bias but work well to avoid the problem of separation. Here we have chosen a simpler solution based on ridge estimators for logistic regression Cessie(1992).

Rather than maximizing $L_j (G | b_j0 , B_j)$ we maximize

$${{L_j}(\left. {\bf{G}} \right|{{\bf{b}}_{j0}},{{\bf{B}}_j})} - \lambda \left( {\left\| {{{\bf{b}}_{j0}}} \right\|^2 + \left\| {{{\bf{B}}_j}} \right\|^2} \right)$$ Changing the values of $\lambda$ we obtain slightly different solutions not affected by the separation problem.

References

Albert,A. & Anderson,J.A. (1984),On the existence of maximum likelihood estimates in logistic regression models, Biometrika 71(1), 1--10. Bull, S.B., Mak, C. & Greenwood, C.M. (2002), A modified score function for multinomial logistic regression, Computational Statistics and dada Analysis 39, 57--74. Firth, D.(1993), Bias reduction of maximum likelihood estimates, Biometrika 80(1), 27--38 Heinze, G. & Schemper, M. (2002), A solution to the problem of separation in logistic regression, Statistics in Medicine 21, 2109--2419 Le Cessie, S. & Van Houwelingen, J. (1992), Ridge estimators in logistic regression, Applied Statistics 41(1), 191--201.

See Also

OrdinalLogBiplotEM,CheckDataSet

Examples

  
data(LevelSatPhd)
dataSet = CheckDataSet(LevelSatPhd)
datanom = dataSet$datanom
olb = OrdinalLogBiplotEM(datanom,dim = 2, nnodos = 10,
            tol = 0.001, maxiter = 100, penalization = 0.2)
model = pordlogist(datanom[, 1], olb$RowCoordinates, tol = 0.001,
        maxiter = 100, penalization = 0.2)
model